I need explicit explanation for this question! Thanks!

For a stock, you are given: i. The current stock price is 90 ii. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2% iii. The stock' s volatility is 20% iv. You use a three-period forward binominal tree to model the movement of the stock price. The length of each period is 3 months You are also given that the continuously compounded risk free rate is 10% Consider a 9 month 90 strike American put on the stock, calculate the risk neutral probability that option will be exercised before maturity Possible Answers A 0.1447 1 0.2756 C 0.3928 D 0.5249 0.7244